Hall-Petch Type Research Articles

Cavity nucleation under time-dependent stress concentrations

Abstract Intergranular cavity nucleation under creep-induced microscale stress concentrations is studied in the framework of the formal theory of nucleation under time-dependent supersaturation presented in an earlier paper. The energetic and kinetic conditions for significant cavity nucleation and the conditions for permanent cavity stability during stress relaxation are established. For a suddenly activated slip/grain boundary interaction the kinetic condition for significant nucleation is operative, constituting a Hall-Petch type relationship for cavitation. Expressions for the total number density of cavities nucleated during a single stress pulse and for the average cavity nucleation rate resulting from a randomly fluctuating stress are derived. The results provide explanations for some observations in creep cavitation not previously understood.

Effect of antimony additions on hardness and tensile properties of directionally solidified Al–Si eutectic alloy

AbstractThe effect of antimony additions on the hardness and tensile properties of Al–Si eutectic alloy has been examined during directional solidification. Antimony, provided that its concentration in the melt was maintained at ~0·1 wt-%, improved the mechanical properties of the eutectics by almost 20–25%, all effects being additive to those that can be gained through increasing the growth velocity of the samples. Mechanical properties were found to correlate directly with the spacing between the silicon particles of the eutectic phase of the solidification structure, a Hall–Petch type relationship existing between the yield strength and silicon particle spacing.MST/653

Effect of grain refinement on the endurance limit of plain carbon steels at various strength levels.

The relationship between the endurance limit and ferrite grain size was investigated in a wide range of ferrite grain sizes using smooth specimens of low carbon steel, medium carbon steel and low alloy steel under rotating bending. It was found that the endurance limit of ferritic pearlitic steel clearly shows the Hall-Petch type relationship when the metallurgical parameters, such as chemical compositions and microstructural morphologies, are the same. The endurance limit can be determined by the additive effect of the strength level of matrix ferrite and the grain refinement. The effect of grain refinement on the endurance limit was constant irrespective of the strength level of matrix microstructure.

Interaction of slip with grain boundary and its role in cavity nucleation

Localized stress evolution resulting from the interaction of slip with a grain boundary is characterized by a superposition of the “internal loading” of a subsystem by dynamic dislocation pile-up and the diffusional relaxation along the grain boundary. The probability of cavity nucleation per stress pulse is evaluated by using a quasi-steady-state extension of the classical nucleation theory. The nominal efficiency of a grain boundary as vacancy source and sink is related to the climb mobility of grain boundary dislocations. The critical stress for cavity nucleation (a Hall-Petch type relationship) is derived, which is related to the effective slip length. Once nucleated, cavities are stable through the transient growth stage. The frequency of slip/grain-boundary interaction and continuous cavity nucleation during creep are discussed by comparing theoretical predictions with the available experimental data.

Tensile strength and flux pinning force of superconducting Nb3Sn compound as a function of grain size

In order to evaluate the influence of grain size on the strength and flux pinning force of the Nb3Sn compound, the microstructure, tensile behaviour and flux pinning force of the bronze-processed Nb3Sn superconducting composite materials were investigated under various heat treatments. It was found that the strength of the Nb3Sn layer has a strong dependency on the grain size and it can be expressed by the Hall-Petch type relation. The flux pinning force was roughly proportional to the inverse grain size, agreeing with the results of former investigations.

Effect of grain size on threshold behavior of small crack in plain carbon steel.

The effects of grain size for improving in fatigue strength was studied on plain carbon steel, with a special emphasis on the critical behavior of the non-propagating crack. It is found from experimental analysis that the endurance limit of plain carbon steel follows the Hall-Petch type relationship in a wide range of ferrite grain sizes. However, the effect of grain refinement on the endurance limit is not so prominent, compared with results already popularly known. Furthermore, an improvement in the fatigue strength of low carbon steel by grain refinement can be associated with the restriction of the length of a critical non-propagating crack, and with an increase of the crack growth resistance of matrix ferrite.

The effect of ferrite grain size and martensite volume fraction on the tensile properties of dual phase steel

The yield strength and tensile strength of dual phase steel are found to follow a Hall-Petch type dependence on the mean free path in ferrite d ƒ , i.e. σ = σ 0 + kd ƒ − 1 2 . The Hall-Petch slope k increases with increasing volume fraction of martensite, V m , in the dual phase in both cases, and σ 0 is independent of V m for yield strength but increases with V m for tensile strength. The effect of ferrite grain size and the martensite volume fraction on the yield strength of a dual phase steel can be explained by extending the dislocation pile-up model to dual phase steels. Also, it is found that the effect of ferrite grain size on yield strength is much stronger than on tensile strength. This naturally leads to a decrease of the yield to tensile ratio with increasing ferrite grain size. The yield ratio approaches a constant value at large ferrite grain size and this limiting value decreases with V m . It is demonstrated that these two observations are predictable from the Hall-Petch equations for the yield strength and tensile strength of the dual phase steel.

The microstructure and mechanical properties of unidirectionally solidified NiSn eutectic alloy

Ni-33.5wt.%Sn (the starting materials were high purity (99.96%) nickel and high purity (99.95%) tin) eutectic alloy was unidirectionally solidified at rates of 0.1−1.8 cm h −1. The microstructure consisted of continous alternating lamellae of a nickel solid solution in an Ni 3Sn matrix. The orientation relationship between the phases was determined by electron diffraction. The interlamellar spacing λ obeyed the relation λ 2R = constant where R is the solidification rate. A transmission electron microscopy study showed that the nickel phase was rich in dislocations concentrated in the vicinity of the phase boundary and contained fine precipitates. The Ni 3Sn phase was free of any precipitation and contained a low density of dislocation pairs. The microstructure remained stable up to 1173 K. The tensile strength is proportional to λ −1 2 and follows a Hall-Petch type of relation. No correlation was found between the compressive properties and R. It is shown that the Griffith brittle fracture theory may be applied to the failure in tension which initiates from cracks in the Ni 3Sn matrix.

Effects of Prior Cold Rolling and Post Temper Rolling on the Properties of Continuously Annealed Low Carbon Dual Phase Steel

The effects of two processing variables, prior cold reduction and temper rolling, on the mechanical properties of a continuously annealed 0.05 pct C low alloy dual phase steel were studied. It was found that cold rolling affected the strength of the dual phase steel through its influence on the recrystallized ferrite grain size. The correlation between yield strength and mean free path in ferrite was shown to follow a Hall-Petch type relationship. Similarly, temper rolling also had a pronounced effect on the yield strength of the steel. The effect was strongly dependent upon the previous overaging treatment; the lower the overaging temperature, the stronger the effect. Basically, the effect of temper rolling on dual phase steel was not much different from that on mild steel and HSLA in terms of the change in yield strength and yield point elongation. Another interesting observation was the influence of quenching rate on the strength of the dual phase steel. A slower quenching rate in the heavier gauge dual phase steel caused pearlite rims to form around martensite colonies and thus decreased the strength of the steel.

Effect of grain size on work hardening in austenitic–ferritic steel

The influence of grain size on the flow stress of a duplex austenitic–ferritic steel was examined at room temperature. Three groups of specimens, the steels in each group containing about the same amount of the phases, i.e. 26, 35, and 47%α, but having different grain sizes, were investigated. As in single phase metals and alloys and two phase dispersion alloys, a relationship of the Hall–Petch type can be used to describe the dependence of flow stress on the grain size of the duplex alloy. The traditional exponent m = 0·5 can be replaced by m = 1. The structural changes of the austenite and ferrite during deformation were observed and the dislocation densities were measured for small strains. Observations by electron microscopy showed that the dislocation density was higher in the vicinity of grain boundaries than within the grains and was not dependent on grain size.

Microstructure and mechanical properties of a quenched and tempered Cr-V dual-phase steel.

An HSLA steel containing 1% Cr and 0.2% V was obtained in a dual phase form by cooling from the austenite field to the (α+γ) range, then quenching into iced brine. The present morphology consists essentially of polygonal ferrite and martensite. It exhibits higher strength than dualphase steel obtained by quenching from the intercritical range. Though this result has been reported before on a similarly treated Fe-Si-C steel, the present steel shows larger ductility. This is due to the effect of Cr and/or V on the interstitial content of ferrite. The yield strength, tensile strength and elongation were observed to vary linearly with the volume fraction of martensite in both quenched and tempered microstructures. Previous equations reported by Onel and Nutting, 12) relating hardness of tempered martensite to its ferrite grain size were found applicable to the present tempered dual phase steel after averaging the free-ferrite and recoveredferrite. Furthermore, the yield strength varies with the average ferrite grain size via a Hall-Petch type relationship.

Cyclic deformation of pearlitic eutectoid rail steel

Cyclic deformation behavior in pearlitic eutectoid steel strongly depends on the interlamellar spacing with cyclic softening in fine pearlite, cyclic hardening in coarse pearlite, and both cyclic softening and hardening depending on the strain amplitude in medium pearlite. Dislocations in cyclically softened specimens were uniformly distributed, while dislocation cells were observed with cyclic hardening. The cell size decreased with increasing strain amplitude. Using the cell size to interlamellar spacing ratios, conditions for cell formation were quantified. Based on dislocation structure observations, mechanisms for cyclic softening and hardening were proposed. Both monotonic and cyclic yield stresses follow Hall-Petch type relations when plotted against interlamellar spacing. Surface fatigue microcrack initiation usually occurred in the ferrite matrix associated with extrusions and intrusions. Most microcracks were almost parallel to the cementite lamellae and oriented between 30 and 90 deg with respect to the tensile axis. Little influence of MnS inclusions on microcrack initiation was noticed.

Mechanical Properties of Polycrystalline TiC

The mechanical properties of fine-grained polycrystalline TiC were studied using both four-point bending and compression tests. The ductile-brittle transition (D-B) temperature in compression was determined to be =800°C and was found to depend on grain size. Yield-point behavior was observed for the first time in fine-grained TiC deformed in compression and was found to depend on grain size and test temperature. The yield stress as a function of grain size can be described by a Hall-Petch type of relation, i.e. yield stress α (grain size)-1/2. The dislocations resulting from deformation in compression at lower temperatures were predominately screw in character, with edge dipoles and dislocation loops being present. As the temperature of deformation was increased, the dipoles and loops were gradually annihilated by climb and the dislocations were observed in the form of hexagonal networks with a much-reduced dislocation density. A plot of log yield stress vs 1/T showed a change in slope, which suggests that two rate-controlling mechanisms are in operation during deformation at different test temperatures. Thermal activation analysis at T = 1050° to 1500°C suggested that the rate controlling mechanism during deformation in this temperature range is associated with cross slip.

Interactive effects of shock loading parameters on the substructure and mechanical properties of nickel and stainless steel

The dislocation density, dislocation cell size and intertwin spacing have been measured in shock-loaded nickel (about 35 μm grain size) along with the dislocation density, intertwin spacing, twin-fault volume fraction and α′ martensite volume fraction in shock-loaded type 304 stainless steel having grain sizes of 14, 38 and 89 μm. The three stainless steel grain sizes and the nickel sample were simultaneously shock loaded in a single experimental sandwich stack of sheet specimens. Single shock loading events were performed at 150, 300 and 450 kbar at 2 μs pulse duration and 450 kbar at 6 μs pulse duration, while a single sandwich was repeatedly shock loaded three times at 150 kbar at 2 μs pulse duration to investigate the effects of multiply shocked substructures. The dislocation density in the stainless steel decreased without exception as the grain size increased, and the α′ martensite volume fraction increased with increasing grain size. The α′ martensite also increased with increasing shock pressure to some extent with increasing (longer) pulse duration. The residual 0.2% offset yield stress followed a Hall-Petch type relation when considering cell size d and intertwin spacing Δ in nickel ( σ∼d −1, σ∼Δ − 1 2 ), while a Hall-Petch type relation was also followed in stainless steel for grain size D and intertwin spacing Δ ( σ∼D − 1 2 , σ∼Δ −1/2 ). It was shown that dislocation cells, twins or twin-faults and martensite all contribute to subgrain refinement and residual shock strengthening. Multiply loaded nickel and type 304 stainless steel exhibited microstructures and residual properties different from single events but were not representative of either additive shock stress or pulse duration. The initial microstructure was observed to influence the residual shock microstructure strongly as expected on the basis of work-hardening considerations. Multiply shocked 304 stainless steel contained a high density of martensite as compared with (equivalent) single shock events (150 kbar, 2 μs), and this was due to the shock loading of existing (initial) twin faults and the interactions of these faults to nucleate and grow martensite within such twin-fault bundles.

Brittleness of high-chromium ferritic stainless steels

1. Ferritic chromium steels with 10–30% Cr and grain size≥grade 8 with cleanness typical of openmelted steels undergo brittle fracture at room temperature. 2. The use of vacuum melting for high-chromium ferritic steels reduces the concentration of impurities (C+N+O) by an order (total concentration of interstitial impurities drops from tenths to hundredths of one percent), which lowers the transition temperature by 130–170° for steels of grade 8 and 220–295° for steels of grade 4. 3. Raising the chromium content from 10 to 30% in both open and vacuum heats raises the transition temperature additively, which is described by the equation T50=k·% Cr+b. 4. The transition temperature of high-chromium ferritic steels, both open and vacuum heats, increases with the grain size, which conforms with a relationship of the Hall-Petch type: T50=M+N·d−1/2.

Deformation of pearlite

Pearlite with its lamellae oriented mainly parallel to the longitudinal direction was prepared by Bolling's method of transformation in a steep temperature gradient. The Fe-0.7 pct Mn-0.9 pct C pearlite was drawn into wire and also into strip in dies designed to minimize macroscopically nonuniform deformation. Cross sections of the drawn wires and strip were examined by conventional and high-voltage transmission electron microscopy and were analyzed by quantitative metallography for a) average interlamellar spacing, b) distribution of interlamellar spacings, and c) orientation relationship between the cementite lamellae and the slip systems in the ferrite. The strength of pearlite is proportional to the reciprocal square root of the average interlamellar spacing, and the proportionality constant analogous to the Hall-Petch constant (k) is related to the strength of the cementite lamellae. If the stress for the propagation of slip through the cementite is assumed constant, a Hall-Petch type of equation can be derived for the strengthening of the pearlite against slip in the ferrite by piled-up groups of dislocations. Evidence for the plastic deformability of cementite is presented; sufficiently thin cementite plates were fully plastic. The exponential strain hardening of drawn pearlitic wires and of rolled pearlite is explained in terms of locally inhomogenous deformation revealed by the lack of fragmentation of the lamellae.

The influence of grain size and composition on the stress-strain behaviour of α-phase in the CuAl system

The stress—strain behaviour of single-phase alloys of CuAl with high Al content has been studied. The flow stress can be described by an equation of Hall—Petch type ρ=ρ oy +Aϵ p +β ϵ p λ 1 2 + k ′ λ where the different contributions can be identified with different hardening mechanisms.

Effect of Grain Boundary Ledges on the Flow Stress in Nickel

In a recent paper1 it was shown that grain boundary ledge structure can be changed by appropriate thermomechanical treatments. Grain boundary ledges are sources of dislocations2. Recently the effects of grain boundaries on the mechanical properties in metals and alloys were studied3,4. For a few years now the structure and properties of grain boundaries and their control have been considered as a means of strengthening polycrystalline materials5,6. Li5 has derived a Hall-Petch type relation in terms of grain boundary dislocation source (ledge) density, m, in the form where L is the grain size, σ0 and α are constants, and G ana b have the usual meaning. The influence of grain boundary ledge density, on the flow stress is considered in this paper.In the present work, pure (99.98%) nickel sheet mill rolled (hot) to 0.022 in. thick was used.

Strengthening of copper by dislocation substructures

Substructural strengthening in pure copper deformed by cold rolling is shown to depend on both the mean free path and the level of nonuniform strain associated with the dislocation substructure. Contributions from the nonuniform strain are particularly important because the mean free path becomes constant after deformations of ∼50 pct R.A., whereas the material continues to work harden. The behavior of the nonuniform strains at large deformations is also found to be closely related to dynamic recovery. Development of an empirical expression for the strengthening in terms of the substructural parameters is shown to lead to a modified Hall-Petch type relation.

Hardness and Recrystallization Behavior of Ag-Ni Sintered Two Phase Alloys Prepared by Cold Drawing

The purpose of this paper is to discuss the hardening mechanisms of Ag-Ni sintered two phase alloys containing fibrous Ni prepared by cold drawing. Deformation behavior during cold drawing and softening behavior during isochronal annealing were studied by hardness measurements.The results are summerized as follows:(1) Ag-Ni alloys containing fibrous Ni were obtained by cold drawing of sintered alloys. The hardness of these alloys was higher than that calculated by the mixing rule based on the hardness of Ag and Ni.(2) In the region of low Ni volume fractions and low reduction, the matrix and secondary phases were deformed with different strain. Deformation in the matrix was larger than that in the secondary phase.(3) Hardening by fine structure and strain hardening were distingusihed. Structural hardening was represented by the Hall-Petch type relation.(4) Ag-Ni alloys containing fibrous Ni had a higher recrystallization temperature than that of Ni. The main cause of this behavior was the inhibition of the strain energy relief due to the fine structure.